The management of the Diners Delight restaurant chain is in theprocess of establishing quality control charts for the time thatits service people give to each customer. Management thinks thelength of time that each customer is given should remain withincertain limits to enhance service quality. For simplicity, the datafrom three samples are displayed below. In each sample, fourservice people were randomly selected, and the customer servicethey provided was observed. The time (in seconds) to service eachcustomer was recorded as below.

Service person	Sample 1 (morning)	Sample 2 (afternoon)	Sample 3 (evening)
#1	201	196	201
#2	198	206	210
#3	206	208	211
#4	195	202	206

• Keep two decimals if not exact, do not round. For example,3.24923... will be kept as 3.24, but the exact value of 0.625 willbe kept as 0.625

1. What is the sample size of this study?  
2. What is the X-bar value of sample 1?  
3. What is the R-value of sample 2?  
4. What is 99.73% (3-sigma) the upper control limit of the X-barchart   and R-chart   ?
5. Assume the established control chart are as follows: X-barchart is [120, 170], and R-chart is [5, 20]. A sample of sixservice personnel was observed, and the following customer servicetimes in seconds were recorded: 180, 125, 110, 145, 156 and 190.What is the sample mean here?   Based on theinformation of sample mean and sample range, and the assumedestablished control chart, please determine whether the sampleprocess is in control or not. (answer Y or N here)

Several complaints recently have been sent to the LA city officeregarding the increasing incidence of congestion on the city’sstreets. The complaints attribute the cause of these traffictie-ups to a lack of synchronization of the traffic lights. Thelights are controlled by a main computer system, and adjusting thisprogram is costly. Therefore, the city is reluctant to change thesituation unless a clear need is shown. During the past threemonths, the office initiated a study and collected 150 data eachmonth at major intersections and identify the # of congestionincidents. The congestion data is shown below.

Month	Congestion Incidents
1	12
2	18
3	15

• Keep 3-decimal if not exact, do not round up. For example,0.24364....will be kept as 0.243
• Both formats, 0.243 or .243, are acceptable

1. What is the sample size of the study?  
2. What is the p-value of sample 1 (month 1)?  
3. What is the p-bar value of the study?  
4. What is the upper control limit, for a 3-sigma qualitystandard, based on the above data?
5. Assume the p-chart for an acceptable traffic congestion rate is[0.02, 0.09], and last month's # of congestions is 203 from a 2300traffic-observation, what is last month's samplep-value?  Does last month's congestion situationacceptable or not, comparing to the assumed p-chart? (answer Y or Nhere)  

A process fills baby formula into bottles with a target of 3ounces ± 0.12 ounce. Two hundred bottles of baby formula from theprocess were sampled. The results showed the average amount of babyformula placed in the bottles to be 3.022 ounces. The standarddeviation of the amounts was 0.035 ounce.

• Keep 3-decimal if not exact, do not round up. For example,0.24364....will be kept as 0.243
• Both formats, 0.243 or .243, are acceptable

1. Determine the value of C_pk for theprocess.  
2. Does it meet the 3-sigma quality control standard? (answer Y orN here)